Engineering B4 pages 582588 Free Vibration A mass is free to oscillate No external forces acting on the mass Amplitude frequency periodall constant Natural Frequency f 0 The frequency of the free vibrations of a system ID: 580763
Download Presentation The PPT/PDF document "Forced vibrations and resonance" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
Forced vibrations and resonance
Engineering: B.4, pages 582-588Slide2
Free Vibration
A mass is free to oscillate
No external forces acting on the mass
Amplitude, frequency, period…all constant
Natural Frequency (
f
0
)
The frequency of the free vibrations of a systemSlide3
Forced Vibrations
Those vibrations that occur when an external force is applied at a regular frequency so that the system vibrates at the same frequency as the force
If the frequency of the applied force is the same as (or close to) the natural frequency of the oscillating system, the amplitude will increase
If the frequency of the applied force is significantly different than the oscillation’s frequency, the amplitude will possibly decrease
External force =
Driving ForceSlide4
Resonance
Occurs when
driving force
is applied at a frequency that matches the natural frequency of the oscillating system.
When damping occurs,
effects are minimized.
When no damping
occurs, maximum amp.Slide5
Examples
Good (beneficial) Resonance
Musical instruments
Earthquake counter-balance (damping to minimize effects!)
Quartz crystals in precision timing devices
LASERs
Cooking in microwave ovens
Destructive Resonance
Building destruction during earthquakes
Tacoma Narrows Bridge collapse
Airplane wings (esp. small aircraft) when strong winds pass
over them:
https://
www.youtube.com/watch?v=iTFZNrTYp3k
https://
www.youtube.com/watch?v=ImSuZjvkATw
Ground Resonance:
https://www.youtube.com/watch?v=-
LFLV47VAbI
https://
www.youtube.com/watch?v=vTRuWgoEFxo
Slide6
What if there’s a resistive external force?
Resistive forces tend to increase in magnitude with increased speed of the system
Always act in opposite direction of motion
Maximum resistive force
at equilibrium point (highest speed)
Zero resistive force
at amplitude (speed = 0)
To oppose the resistive force, the oscillating system does work, transfers energy out of the system
Amplitude decreasesSlide7
Damping
The effect on a system when a resistive force is acting on the oscillationSlide8
Under-Damping
Light damping
Rate of damping (the rate of decrease of the amplitude) is an exponential decay
The ratio of the amplitudes at half-period intervals remains constant
Frequency remains constantSlide9
Critical Damping
“Heavy damping”
System returns to equilibrium position in shortest possible time
System does NOT oscillate past the equilibrium point before stopping
Examples: car suspensions; some fire doors; shock absorbers of all sortsSlide10
Over-Damped
System stops oscillating quickly, but takes longer to get to the equilibrium point than a critically damped system.Slide11
Graphical comparison of damping effectsSlide12
Q factor
Numerical,
unitless
quantity
High damping Light DampingSlide13
Q Factor
“Quality” Factor
The quantifiable criterion that allows us to asses the amount of resonance that will occur
OR
See page 585 for an explanation of how these are equivalent expressions.
Slide14
Q Factor for Mechanical Oscillators
Oscillator
Q Factor
Critically damped door
0.5
Mass
on spring
50
Simple
Pendulum
200
Oscillating
quartz crystal
30000
A sample list of Q factor values. These are not exact quantities for every situation.Slide15
Practice Problem:
An electrical pendulum clock has a period of 1.0 s. An electrical power supply of 25
mW
maintains its constant amplitude. As the pendulum passes its equilibrium position it has kinetic energy of 40.0
mJ
.
Turn and talk: how do these quantities apply to the Q factor relationship?
Calculate
the Q factor for this pendulum clockSlide16
Solution:
An electrical pendulum clock has a period of 1.0 s. An electrical power supply of 25
mW
maintains its constant amplitude. As the pendulum passes its equilibrium position it has kinetic energy of 40.0
mJ
.
Is this system underdamped, overdamped, or critically damped? How do you know?
Slide17
Reading assignment:
Read about Barton’s Pendulums and the Nature of Science examples of resonance on pages 586-587 of your textbook.